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SageMath
E = EllipticCurve("dx1")
E.isogeny_class()
Elliptic curves in class 62400.dx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62400.dx1 | 62400o2 | \([0, -1, 0, -14586000833, -678030687590463]\) | \(-134057911417971280740025/1872\) | \(-4792320000000000\) | \([]\) | \(32256000\) | \(3.9884\) | |
| 62400.dx2 | 62400o1 | \([0, -1, 0, -22739393, -45716567103]\) | \(-198417696411528597145/22989483914821632\) | \(-150663881784175047475200\) | \([]\) | \(6451200\) | \(3.1837\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 62400.dx have rank \(1\).
Complex multiplication
The elliptic curves in class 62400.dx do not have complex multiplication.Modular form 62400.2.a.dx
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
